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Solving Equations by Multiplying or Dividing (3-4) Definition: Inverse operations “undo” each other _______________ and _______________ are inverse operations, because they “undo” each other. Division Property of Equality: If you divide the same number for each side of an equation, the two sides remain equal Ex. 15 = 15 Ex. 3m = 24 __________= ___________ __________= ___________ _____ = _____ _____ = _____ Multiplication Property of Equality: If you multiply the same number for each side of an equation, the two sides remain equal Ex. 5=5 Ex. __________= ___________ x=5 2 __________= ___________ _____ = _____ _____ = _____ To Solve Equations you use the Division Property and Multiplication Property of Equality to “UNDO” what had been added to or subtracted from x, to find the value of the variable Solve each equation. Check your solution. Ex. m = 16 (Multiplication Prop) -4 _______ = _______ Check: (Substitute) Ex. (Division Property) _______ = _______ Check: (Substitute) (Solution) m = 16 -4 _______ = _______ 4x = 28 Ex. (Solution) 4x = 28 _______ = _______ x = -5 2 (Multiplication Prop) _______ = _______ Check: (Substitute) Ex. x = -5 2 _______ = _______ -2y = -24 (Division Property) _______ = _______ Check: (Substitute) (Solution) (Solution) -2y = -24 _______ = _______ *x is the same as 1x, so –x is the same as __ Ex. -x = 8 (Division Property) _______ = _______ Check: (Substitute) (Solution) -x = 8 _______ = _______ Ex. -x = -5 (Division Property) _______ = _______ Check: (Substitute) (Solution) -x = -5 _______ = _______